Computability: Computable Functions Logic and the Foundations of Math (Wadsworth&Brooks/Cole Mathematics Series) | 
| Authors: Richard .l. Epstein, Walter Alexandr Carnielli
Publisher: Chapman & Hall/CRC
Category: Book
List Price: $164.95
Buy New: $97.56
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New (13) Used (6) from $39.97
Avg. Customer Rating:  2 reviews
Sales Rank: 1865005
Media: Hardcover
Edition: 1
Number Of Items: 1
Pages: 320
Shipping Weight (lbs): 1.6
Dimensions (in): 9.7 x 7.4 x 0.8
ISBN: 0534103561
Dewey Decimal Number: 511.3
EAN: 9780534103569
ASIN: 0534103561
Publication Date: May 15, 1990
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Condition: Brand new item. Not previously owned. Not a remainder. Your satisfaction is guaranteed.
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Product Description
This book should be of interest to intermediate mathematics undergraduates; postgraduates in theoretical computer science/philosophy of mathematics.
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| Customer Reviews:
 Worth buying a used copy. June 15, 2005
6 out of 6 found this review helpful
This book is half mathematics and half discussion. Parts 2 & 3 cover the material for an integrated, introductory course in computability theory and logic (the primitive recursive functions, mu-recursive functions and Turing machines and their equivalence, first-order logic, some formal number theory, and Godel's first and second incompleteness theorems). Parts 1 & 4 are given to philosophical discussion and (to a lesser extent) historical background. The longest chapters are one examining Church's thesis and one on intuitionist/constructivist views of mathematics. Overall the book is clearly written and well organized, and it contains interesting selections from the writings of prominent figures in the foundations of mathematics throughout.
Adjoined to the end is a 25 page timeline, surveying 1834-1970. This is quite neat, but I wish it had been longer. The book should be useful both to people new to computability & logic, as well as those with some previous background, but the target audience is probably those with an interest in philosophy of mathematics.
1)Beginners- Its helpful to learn computability theory and logic together. But that's a lot of ground for a single volume to cover, and since this one is particularly short (parts 2&3 run only 157 pages), some of the material is only loosely sketched. I'd recommend a more thorough, grind-the-gory-details book as a central text and that you use Epstein & Carnielli as a supplement, providing a clean overview of whats going on. The philosophical material will either illuminate the motivation for the mathematical constructions, or will just muddy the waters for you, depending on your temperment. This can be skipped or skimmed if you want, but that would defeat the unity and aesthetic of the book. Be warned some of the historical writings will be hard for a beginner, especially as E&C dont take enough time to set the stage for them.
2)More experienced readers will enjoy the selections from Hilbert, Godel, Turing, Post, Brouwer and others. These arent the complete papers (see Davis or van Heijenoort for those), just choice passages. I enjoyed the amount of philosophical material included- more than your usual math book, but short enough to keep from getting tedious or slipping into general philosophy. Parts 2&3 form a succinct review of the basics if you need to brush up.
 when critical thinking, computer and math meet at one April 14, 2001
1 out of 4 found this review helpful
this book takes you into the world of basic pure math. it covers the basic elemects of math such as sets, functions, and proofs. but what is really making this book great and far apart from other similiar books is its elaboration of recursive function and computability, and i find it interesting.
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